A Test of the Collisional Dark Matter Hypothesis from Cluster Lensing

Spergel & Steinhardt proposed the possibility that the dark matter particles are self-interacting, as a solution to two discrepancies between the predictions of cold dark matter models and the observations: first, the observed dark matter distribution in some dwarf galaxies has large, constant-density cores, as opposed to the predicted central cusps; and second, small satellites of normal galaxies are much less abundant than predicted. The dark matter self-interaction would produce isothermal cores in halos, and would also expel the dark matter particles from dwarfs orbiting within large halos. However, another inevitable consequence of the model is that halos should become spherical once most particles have interacted. Here, I rule out this model by the fact that the innermost regions of dark matter halos in massive clusters of galaxies are elliptical, as shown by gravitational lensing and other observations. The absence of collisions in the lensing cores of massive clusters implies that any dark matter self-interaction is too weak to have affected the observed density profiles in the dark-matter dominated dwarf galaxies, or to have eased the destruction of dwarf satellites in galactic halos. If $s_x$ is the cross section and $m_x$ the mass of the dark matter particle, then s_x/m_x < 10^{-25.5} \cm^2/\gev.Comment: to appear in ApJ, January 1 200

The Einstein Ring 0047-2808 Revisited: A Bayesian Inversion

In a previous paper, we outlined a new Bayesian method for inferring the properties of extended gravitational lenses, given data in the form of resolved images. This method holds the most promise for optimally extracting information from the observed image, whilst providing reliable uncertainties in all parameters. Here, we apply the method to the well studied optical Einstein ring 0047-2808. Our results are in broad agreement with previous studies, showing that the density profile of the lensing galaxy is aligned within a few degrees of the light profile, and suggesting that the source galaxy (at redshift 3.6) is a binary system, although its size is only of order 1-2 kpc. We also find that the mass of the elliptical lensing galaxy enclosed by the image is (2.91$\pm$0.01)$\times10^{11}$ M_{\sun}. Our method is able to achieve improved resolution for the source reconstructions, although we also find that some of the uncertainties are greater than has been found in previous analyses, due to the inclusion of extra pixels and a more general lens model.Comment: Accepted for publication in Ap

Compton Heating of the Intergalactic Medium by the Hard X-ray Background

High-resolution hydrodynamics simulations of the Ly-alpha forest in cold dark matter dominated cosmologies appear to predict line widths that are substantially narrower than those observed. Here we point out that Compton heating of the intergalactic gas by the hard X-ray background (XRB), an effect neglected in all previous investigations, may help to resolve this discrepancy. The rate of gain in thermal energy by Compton scattering will dominate over the energy input from hydrogen photoionization if the XRB energy density is 0.2x/ times higher than the energy density of the UV background at a given epoch, where x is the hydrogen neutral fraction in units of 1e-6 and is the mean X-ray photon energy in units of m_ec^2. The numerical integration of the time-dependent rate equations shows that the intergalactic medium approaches a temperature of about 1.5e4 K at z>3 in popular models for the redshift evolution of the extragalactic background radiation. The importance of Compton heating can be tested experimentally by measuring the Ly-alpha line-width distribution as a function of redshift, thus the Lyman-alpha forest may provide a useful probe of the evolution of the XRB at high redshifts.Comment: LaTeX, 10 pages, 2 figures, final version to be published in the Ap

Evolution of Structure in the Intergalactic Medium and the Nature of the Ly-alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly non-linear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN field has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluc- tuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a non-standard CDM model with Omega=1, h=0.5 and \Gamma=0.3, and the other is a low density flat model with a cosmological constant(LCDM), with Omega=0.4, Omega_Lambda=0.6 and h=.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z=4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z=4 down to at least z=2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. (This is an abreviated abstract; the complete abstract is included with the manuscript.)Comment: Wrong Fig. 10 is corrected. Our custom made postscript is available at ftp://hut4.pha.jhu.edu/incoming/igm, or contact Arthur Davidsen ([email protected]) for nice hardcopies; accepted for publication in Ap

The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters

Recent observations support the idea that nuclear black holes grew by gas accretion while shining as luminous quasars at high redshift, and they establish a relation of the black hole mass with the host galaxy's spheroidal stellar system. We develop an analytic model to calculate the expected impact of mergers on the masses of black holes in massive clusters of galaxies. We use the extended Press-Schechter formalism to generate Monte Carlo merger histories of halos with a mass 10^{15} h^{-1} Msun. We assume that the black hole mass function at z=2 is similar to that inferred from observations at z=0 (since quasar activity declines markedly at z<2), and we assign black holes to the progenitor halos assuming a monotonic relation between halo mass and black hole mass. We follow the dynamical evolution of subhalos within larger halos, allowing for tidal stripping, the loss of orbital energy by dynamical friction, and random orbital perturbations in gravitational encounters with subhalos, and we assume that mergers of subhalos are followed by mergers of their central black holes. Our analytic model reproduces numerical estimates of the subhalo mass function. We find that the most massive black holes in massive clusters typically grow by a factor ~ 2 by mergers after gas accretion has stopped. In our ten realizations of 10^{15} h^{-1} Msun clusters, the highest initial (z=2) black hole masses are 5-7 x 10^9 Msun, but four of the clusters contain black holes in the range 1-1.5 x 10^{10} Msun at z=0. Satellite galaxies may host black holes whose mass is comparable to, or even greater than, that of the central galaxy. Thus, black hole mergers can significantly extend the very high end of the black hole mass function.Comment: 13 pages, 7 figures, accepted for publication in The Astrophysical Journa

Lyman alpha absorption lines from mini pancakes

[Abridged abstract:] Recent numerical simulations show that many \lyal absorption lines of column densities \nha \la 10^{15} cm$^{-2}$ are produced in transient, mini pancakes. Such pancakes are modeled here, approximating the initial perturbation leading to the formation of the pancake as a single sinusoidal wave. The density and temperature profiles of the gas in the pancake are determined for $z_c \sim 3$, where $z_c$ is the collapse redshift. The \lyal absorption line profiles for a line of sight through the pancake are then calculated. The absorption lines in general have wings signifying bulk motions in the gas. It is shown that the deviation from a single Voigt profile is large for small H I column density lines, in which the effect of bulk motions is large. For lines with \nha > 10^{13} cm$^{-2}$, high temperature tend to wash out the signatures of bulk motion. The analytical modeling of mini pancakes associated with \lyal forest lines --- with 10^{13} \la \nha \la 10^{15} cm$^{-2}$---gives the corresponding mass scales. It is shown here that, for typical values of cosmological parameters, absorption lines with \nha \sim 10^{14} cm$^{-2}$ correspond to structures with baryonic mass of $M_b \sim 10^{10}$ M$_{\odot}$ with an overdensity of $\sim 10$ at $z \sim 3$. The value of \nha can change by a factor $\sim 3$ in the course of evolution of the pancake in time. It is also shown that there is an upper limit to \nha from a pancake due to the slow recombination rate and the importance of collisional ionization at high temperatures. Mini pancakes do not give rise to \lyal lines with \nha \ga 10^{14.5} cm$^{-2}$, for \j21=1 and $\Omega_{IGM} \sim 0.03$.Comment: Latex with aaspp4.sty (25 pages), 6 figures, Accepted for publication in The Astrophysical Journa

Probing the Slope of Cluster Mass Profile with Gravitational Einstein Rings: Application to Abell 1689

The strong lensing modelling of gravitational ``rings'' formed around massive galaxies is sensitive to the amplitude of the external shear and convergence produced by nearby mass condensations. In current wide field surveys, it is now possible to find out a large number of rings, typically 10 gravitational rings per square degree. We propose here, to systematically study gravitational rings around galaxy clusters to probe the cluster mass profile beyond the cluster strong lensing regions. For cluster of galaxies with multiple arc systems, we show that rings found at various distances from the cluster centre can improve the modelling by constraining the slope of the cluster mass profile. We outline the principle of the method with simple numerical simulations and we apply it to 3 rings discovered recently in Abell~1689. In particular, the lens modelling of the 3 rings confirms that the cluster is bimodal, and favours a slope of the mass profile steeper than isothermal at a cluster radius \sim 300 \kpc. These results are compared with previous lens modelling of Abell~1689 including weak lensing analysis. Because of the difficulty arising from the complex mass distribution in Abell~1689, we argue that the ring method will be better implemented on simpler and relaxed clusters.Comment: Accepted for publication in MNRAS. Substantial modification after referee's repor

The Observed Probability Distribution Function, Power Spectrum, and Correlation Function of the Transmitted Flux in the Lyman-alpha Forest

A sample of eight quasars observed at high resolution and signal-to-noise is used to determine the probability distribution function (PDF), the power spectrum, and the correlation function of the transmitted flux in the \lya forest, in three redshift bins centered at z=2.41, 3.00, and 3.89. All the results are presented in tabular form, with full error covariance matrices to allow for comparisons with any numerical simulations and with other data sets. The observations are compared with a numerical simulation of the \lya forest of a Lambda-CDM model with Omega=0.4, known to agree with other large-scale structure observational constraints. There is excellent agreement for the PDF, if the mean transmitted flux is adjusted to match the observations. A small difference between the observed and predicted PDF is found at high fluxes and low redshift, which may be due to the uncertain effects of fitting the spectral continuum. Using the numerical simulation, we show how the flux power spectrum can be used to recover the initial power spectrum of density fluctuations. From our sample of eight quasars, we measure the amplitude of the mass power spectrum to correspond to a linear variance per unit ln(k) of $\Delta^2_\rho(k)=0.72\pm0.09$ at k=0.04(km/s)^{-1} and z=3, and the slope of the power spectrum near the same k to be $n_p=-2.55\pm0.10$ (statistical error bars). The results are statistically consistent with Croft et. al. (1999), although our value for the rms fluctuation is lower by a factor 0.75. For the Lambda-CDM model we use, the implied primordial slope is $n=0.93\pm0.10$, and the normalization is $\sigma_8=0.68+1.16(0.95-n)\pm0.04$.Comment: submitted to Ap